Patients receive sirolimus orally (PO) two hours before or after grapefruit juice on day -2, cisplatin intravenously (IV) on day 1 and gemcitabine hydrochloride IV over 30 minutes on days 1 and 8. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients undergo cystectomy as clinically appropriate after 1-4 courses of treatment.